General nucleation theory with inhibition for chemically reacting systems

Abstract

We present a general theoretical model of nucleation based on the Becker-Döring kinetic scheme, according to which clusters grow and shrink by one-step aggregation and fragmentation processes. Our model includes the catalytic effects of clusters on the rate of formation of other clusters, which we propose as the microscopic mechanism underlying secondary nucleation; the rôle of a precursor, or source chemical species, which spontaneously decays to form the nucleating material; and an inhibitor which hinders the growth of clusters beyond a certain threshold size. A systematic procedure is developed for extracting from the full model, which comprises an infinite set of differential equations, a low dimensional dynamical system containing only a few key equations which determine the experimentally measurable macroscopic behaviour of the system. From these macroscopic equations it is possible to deduce the most important elements of the reaction scheme, and to isolate the rate-determining stages. One realization of this reduced model, motivated by an application to cement hydration, is solved in a particular asymptotic limit, and the results are shown to compare well with experimental data.